Question: A manufacturing plant earned $\$80$ per man-hour of labor when it opened. Each year, the plant earns an additional $5\%$ per man-hour. Write a function that gives the amount $A(t)$ that the plant earns per man-hour $t$ years after it opens. $A(t)=$
Solution: Earning an additional $5\%$ means the manufacturing plant keeps the original $100\%$ and earns $5\%$ more, for a total of $105\%$. So each year, the amount the plant earns per man-hour is multiplied by $105\%$, which is the same as a factor of $1.05$. If we start with the initial amount, $\$80$, that the plant earned per man-hour, and keep multiplying by $1.05$, this function gives us the amount $A(t)$ that the plant earns per man-hour $t$ years after it opens: $A(t)=80\cdot1.05^t$